week 6

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Group member:
Mohd.Yuhalis
Mohd. Syuhada
Elly Stephen
Corbin Atek

Question 3

(A).
Convert the following first-order sentence into Conjunctive Normal Form (CNF):

1.JPG


(B).
Determine whether the following is a valid inference in first-order logic using resolution:
3.jpg
2.JPG
it is a valid inference.


(C). Show using the truth table method that the following inference is valid:
¬(¬P˄P)˄P

5.jpg





(D). Repeat (c) using resolution. In this case, we want to show:
4.jpg


1.¬[¬(¬P˄P)˄P]

2.¬ ¬(¬P˄P)˅¬P

3.(¬P˄P)˅¬P

4.¬P˄(P˅¬P)

Clausal form of ¬[¬(¬P˄P)˄P] is{¬P,(P˅¬P)}

1.¬P [¬Conclusion]

2. (P˅¬P) [¬Conclusion]

3. P [1,2: Resolution]

4. [] [1,3: Resolution]